I've heard this effect with headphones Hifiman Arya and 1000se, Kennerton Thekk and Wodan, Dan Clark Ether С Flow with almost all high-resolution music tracks.
First of all, in complex symphonic works.
And I'm afraid that this effect has nothing to do with the "lack of power" - Fiio K9 Pro has quite enough power.
This effect is more likely due to the way the device amplifies sound, which is not ideal.
If you use the Fiio K9 Pro as a standalone DAC, by connecting a third-party headphone amplifier with good quality to its output
(for example, I have connected the Singxer SA-1 and the Aune S17 Pro),
the sound experience improves significantly. This is why I believe that the amplification component has its limitations.
P.S. Nothing personal, Fiio K9 Pro is still one of the best devices in its price range, but it does have some objective limitations that should be taken into account.